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Optical Engineering

Quality investigation of the phase-conjugate mirror based on four-wave mixing

Zdeněk Bouchal, Jan Peřina

Published Jan 1, 1995• 4 citations
Publisher

Abstract

The quality of the optical phase conjugation, realized by means of the four-wave mixing in Kerr-like media, is examined. The fidelity of the generated replica of a signal field is investigated in suitable approximations and related problems are solved applying the Fourier transformation. The presented methods are based on the derivation of integro-differential mode equations valid for general conditions, including interaction of polych romatic nonparaxial waves.

DOI
10.1117/12.184106

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The quality of the optical phase conjugation, realized by means of the four-wave mixing in Kerr-like media, is examined. The fidelity of the generated replica of a signal field is investigated in suitable approximations and related problems are solved applying the Fourier transformation. The presented methods are based on the derivation of integro-differential mode equations valid for general conditions, including interaction of polych romatic nonparaxial waves.
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The phase-conjugate field fidelity in backward-going four-wave mixing, based on the diffraction model solvable analytically, is investigated. The method assumes interaction of the non-depleted infinite plane pump waves with the spatially limited probe and signal waves inside the nonlinear medium. Solutions are obtained applying the Fourier transformation and the Green function technique under various boundary conditions for coupled wave equations. The probe and its phase-conjugate waves are defined by using a complex phase formulation including both the phase variation and amplitude modulation. It is shown that the analysed approach can involve assumptions leading to the ideal or distorted phase conjugation.
Optical phase conjugation by four-wave mixing in a Kerr medium is considered. Two strong counterpropagating lasers pump a nonlinear medium in which they excite the third-order polarization. Mixing with a weak incident field then generates the phase-conjugated image of that field. It is shown how the polarization of the pumps and the tensorial nature of the nonlinear interaction can be accounted for by a geometrical polarization tensor. The electric field is shown to obey two coupled wave equations, which couple a positive- and negative-frequency component of the field. These wave equations allow plane-wave solutions, and we derive the dispersion relation for the wave vectors of these modes. By matching the field of such a mode across the boundaries of the medium to an external incident field, we are able to obtain analytically the Fresnel coefficients for reflection and transmission. Our expressions reduce to earlier results in the appropriate limits.